How many colors are there? A lot, as this atlas by Tauba Aurebach illustrates:

american artist tauba auerbach presents the 8 x 8 x 8-inch hard-back cubes illustrating the RGB color scheme in a page-by-page medium. a digital offset print on paper with airbrushed cloth cover and book edges create a colorful reference volume of all the colors in existence.

Also this book is clearly not representing all the visible colors, let alone all the colors in existence. Subtractive color (like printing) has a smaller color gamut than additive color (like a computer monitor), although there is some overlap between the two.